What's a good beginner resource to learn group theory?

Question

I'm interested in learning about the basics of group theory. My background is in statistics so I have barely any knowledge about group theory. I've had some work with proofs and I have also taken classes at university such as multivariable calculus, linear algebra, and differential equations. Any beginner resource would be helpful but nothing too technical.

Answer 1

I'm working on a M.S. in stats and have a very similar background to yours. I am not a fan of Dummit and Foote - the first chapter I found a nightmare to read through myself and I could not get past how dense and terse it was. I've also read Pinter's text and it's good for summarization, but it's not something that really engages me with the subject.

Ultimately, of all of the abstract algebra books I've read, I would have to recommend Abstract Algebra: Theory and Applications by Judson, which the author has made available for free online. Here's an excerpt from an MAA review for this text by Thron:

For many students, abstract algebra is the most daunting of math classes. Many students (particularly those who do not have a strong theoretical bent) see abstract algebra as symbol-twiddling with no apparent rhyme or reason. To them, group theory proofs are just so many rabbits pulled from hats.

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The book’s presentation should be interspersed with numerous, easily-worked examples. The exercises should be progressive, with a generous number of relatively easy problems for student practice. Practical applications of abstract algebra should figure prominently.

Of all the prospective texts I looked at from the standpoint of these requirements, Thomas Judson’s Abstract Algebra: Theory and Applications (AATA) was the best. (The fact that it was free was an added bonus.) The level was non-threatening, and the order and presentation of topics seemed perfect for what I was looking for. The “Preliminaries” chapter begins with several pointers on reading and writing proofs — vital background knowledge that most a abstract algebra books take for granted. Next, the book covers sets and equivalence relations in a way that bridges from familiar material to a more abstract setting. In the chapters dealing with groups, there are entire sections devoted to the integers mod n, symmetries, and complex numbers.

If you don't like Judson, I would try Fraleigh's text: A First Course in Abstract Algebra, 7th Edition.

Answer 2

Dummit and Foote is a classic, but I found "A book of abstract algebra" more motivating and I wish I would've started with that one.